The present invention relates to a method and apparatus for determining the cerebral state of a patient using a measure of the complexity of the EEG signal, such as the spectral entropy of the signal. More particularly, the present invention relates to a method and apparatus for accurately making such determination when artifacts and/or burst suppression is present in the EEG signal through the use of a generalized spectral entropy of the EEG signal. The present invention may be used in conjunction with the teachings in earlier U.S. patent application Ser. No. 09/688,891, filed Oct. 16, 2000, now U.S. Pat. No. 6,731,975, assigned to a common assignee, which application is incorporated herein by reference.
One application of the method and apparatus of the present application is determining the extent of hypnosis of a patient resulting, for example, from the administration of an anesthetic agent. That extent is often termed the “depth of anesthesia.” In a simplistic definition, anesthesia is an artificially induced state of partial or total loss of sensation or pain, i.e. analgesia. For most medical procedures the loss of sensation is accompanied by a loss of consciousness on the part of a patient so that the patient is amnestic and is not aware of the procedure. The “depth of anesthesia” generally describes the extent to which consciousness is lost following administration of an anesthetic agent.
A typical electroencephalogram, or EEG, obtained from electrodes applied to the scalp and forehead of a patient is shown in FIG. 1. A macro characteristic of EEG signal patterns is the existence of broadly defined low frequency rhythms or waves occurring in certain frequency bands. Four such bands are recognized: Delta (0.5-3.5 Hz), Theta (3.5-7.0 Hz), Alpha (7.0-13.0 Hz) and Beta (13.0-32.0 Hz). Alpha waves are found during periods of wakefulness and may disappear entirely during sleep. The higher frequency Beta waves are recorded during periods of intense activation of the central nervous system. The lower frequency Theta and Delta waves reflect drowsiness and periods of deep sleep. Even higher frequency EEG patterns than those described above have been investigated, although measurements are difficult due to very low amplitudes of these high frequency waves.
By analogy to the depth of sleep, it can be said that the frequency of the EEG will decrease as the depth of anesthesia increases, while the magnitude of the signal initially often increases. However, this gross characterization is too imprecise and unreliable to use as an indication of such a critical medical aspect as the extent of hypnosis. Further, EEG signal changes during anesthesia may not fully correlate with changes in the hypnotic state of the patient. For example, it has been reported that in a 12-18 Hz frequency band, EEG activity initially increases as anesthetic agents are administered and only thereafter decreases as anesthesia deepens.
During deep sleep or anesthesia, the EEG signal may develop a pattern of activity which is characterized by alternating periods or “bursts” of normal, or high frequency and amplitude, voltage signals and periods of low or no voltage, which periods are termed those of “suppression.” See FIG. 2. The extent of this phenomenon can be expressed as a “burst suppression ratio (BSR)” which is an EEG parameter describing the time the EEG voltage is in the suppressed state as a fraction of a sampling period. The burst suppression ratio gives a rough indication of the depth of anesthesia: a high burst suppression ratio corresponding to a deeper level of anesthesia than does a low burst suppression ratio.
The limitations of direct analysis of EEG signals has led to the investigation and use of other techniques to study EEG waveforms to ascertain the underlying condition of the brain, including the depth of anesthesia to which a patient is subjected.
Some of the techniques by which EEG signals can be analyzed in an effort to determine the depth of anesthesia are well described in Ira J. Rampil, A Primer for EEG Signal Processing in Anesthesia, Vol. 89, Anesthesiology No. 4, pgs. 980 et seq., October 1998. Prefatory to the use of such analysis techniques, the EEG signals are typically subjected to analog to digital signal conversion by sequentially sampling the magnitude of the analog EEG signals and converting same to a series of digital data values. The sampling is typically carried out at a rate of 100 Hz or greater. The digital signals are stored in the magnetic or other storage medium of a computer and then subjected to further processing to ascertain the underlying state of the brain. Such processing typically uses sets of sequential EEG signal samples or data points representing a finite block of time, commonly termed an “epoch.” The analysis of the data is usually carried out on a moving average basis employing given data points and a certain number of backward data points.
One EEG analysis technique is to examine, in some meaningful way, how the voltage of an EEG signal changes over time. Such an analysis is termed a “time-domain analysis.” Because of its generally random nature, an EEG signal is not a deterministic signal. This means that it is not possible to exactly predict future values of the EEG from past values in the manner that, for example, the shapes of past QRS complexes in an ECG signal can be used to predict future values for analytical and diagnostic purposes. Thus, while certain statistical characteristics of random signals, such as an EEG, can be determined and used for analytical purposes, time-domain based EEG analysis methods have not proven greatly successful in clinical applications since the results do not behave in a completely consistent manner. Time-domain based analysis has, however, been used in the study and quantification of burst suppression in the EEG signal.
A second approach to analyzing EEG waveforms examines signal activity as a function of frequency, i.e. a “frequency-domain analysis.” It has long been recognized that complex waveforms, such as EEG signals, can be decomposed, or transformed, into a plurality, or spectrum, of simple sine or cosine waves of various frequencies, amplitudes, and phases. Frequency-domain spectra can be obtained from sequential time-domain EEG signal data by a Fourier transform. Frequency-domain analysis analyzes the spectrum of frequency signals obtained from the transform to determine characteristics and features occurring in wave forms having the various frequencies of the spectrum. Several parameters relating frequency-domain EEG signal data to the hypnotic state of a patient have been developed.
For clinical use, it is desirable to simplify the results of EEG signal analysis of the foregoing, and other, types into a workable parameter that can be used by an anesthesiologist or anesthetist in a clinical setting when attending the patient. Ideally, what is desired is a simple, single parameter or index that quantifies the depth of anesthesia on a consistent, continuous scale extending from full alertness to maximally deep, but reversible, hypnosis. To be fully useful such a scale should maintain its consistency, notwithstanding the differing pharmacological effects of different anesthetic agents, as well as the differing physiologies of different patients. The scale should rapidly respond to changes in the depth of anesthesia in the patient.
In the search for such a parameter, an approach to the analysis of electroencephalographic signals that is receiving increased attention is to examine and quantify the regularity or irregularity of the highly random EEG signals. This approach is based on the premise that neuronal systems, such as those of the brain, have been shown to exhibit a variety of non-linear behaviors so that measures based on the non-linear dynamics of the EEG signal should allow direct insight into the state of the underlying brain activity.
For example, it is known that developmental factors such as maturation (John et al, Development Equations for the EEG, Science, 210, (1980) pgs. 1255-1258 and Alvarez et al., On the Structure of EEG Development, Electroenceph, Clin. Neurophysiol., 1989, 73:10-19) and attention (Dongier et al. Psychological and Psychophysiological States in A. Rémond (Ed), Handbook of Electroenceph. Clin. Neurophysiol., Vol. 6A, Elsevier, Amsterdam, 1976: pgs. 195-254) increase the irregularity of the EEG signal. Concentration on a particular mental task has been shown to result in a greater degree of local desynchronization of EEG (Pfurtscheller et al., Event-related EEG/MEG Synchronization and Desynchronization: Basic Principles, Clinical Neurophysiology 110 (1999) pgs. 1842-1857, Inoye et al. Quantification of EEG Irregularity by use of the Entropy of the Power Spectrum, Electro-encephalography and Clinical Neurophysiology, 79 (1991) pgs. 204-210). These findings suggest that an active cortex of the brain generally has a more irregular EEG patterns than an inactive cortex.
There are a number of concepts and analytical techniques directed to quantifying the irregularity and complex nature of random or stochastic signals such as the EEG. One such concept is entropy. Entropy, as a physical concept, is related to the amount of disorder in a physical system. When used in information theory and signal analysis, entropy addresses and describes the irregularity complexity, or unpredictability characteristics of a signal. In a simple example, a signal in which sequential values are alternately of one fixed magnitude and then of another fixed magnitude has an entropy of zero, i.e. the signal is completely regular and totally predictable. A signal in which sequential values are generated by a random number generator has greater complexity and a higher entropy.
Applying the concept of entropy to the brain, the premise is that when a person is awake, the mind is full of activity and hence the state of the brain is more complex. Since EEG signals reflect the underlying state of brain activity, this is reflected in relatively more “irregularity” or “complexity” in the EEG signal data, or, conversely, in a low level of “order.” As a person falls asleep or is anesthetized, the brain function begins to lessen and becomes more orderly and regular. As the activity state of the brain changes in such circumstances, it is plausible to consider that this will be reflected in the EEG signals by a relative lowering of the “irregularity” or “complexity” of the EEG signal data, or conversely, increasing “order” in the signal data. When a person is awake, the EEG data signals will have higher entropy and when the person is asleep the EEG signal data will have a lower entropy.
With respect to anesthesia, an increasing body of evidence shows that EEG signal data contains more “order”, i.e. less “irregularity”, and lower entropy, at higher concentrations of an anesthetic agent, i.e. greater depth of anesthesia, than at lower concentrations. At a lower concentration of anesthetic agent, the EEG signal has higher entropy. This is due, presumably, to lesser levels of brain activity in the former state than in the latter state. See “Stochastic complexity measures for physiological signal analysis” by I. A. Rezek and S. J. Roberts in IEEE Transactions on Biomedical Engineering, Vol. 4, No. 9, September 1998 and Bruhn, et al. “Approximate Entropy as an Electroencephalographic Measure of Anesthetic Drug Effect during Desflurane Anesthesia”, Anesthesiology, 92 (2000), pgs. 715-726. See also H. Viertiö-Oja et al. “New method to determine depth of anesthesia from EEG measurement” in J. Clin. Monitoring and Comp. Vol. 16 (2000) pg. 16 which reports that the transition from consciousness to unconsciousness takes place at a universal critical value of entropy which is independent of the patient.
The pertinence of the concept of entropy to the conscious and unconscious states of the brain is also supported in recent theoretical work (see Steyn-Ross et al., Phys. Rev. E60 1999, pgs. 7229-7311) which applies thermodynamic theory to the study of the brain. This work points to the conclusion that when a patient undergoing anesthetization passes from the conscious state to the unconscious state, a thermodynamic phase transition of the neural system of the brain takes place which is roughly analogous to the liquid-solid phase change occurring when water freezes into ice. During the process of freezing, an amount of entropy, proportional to the latent heat of the process, is removed so that water and ice have different entropies. According to the theory, the conscious and unconscious states of the brain should have distinct, different values of entropy. While thermodynamical entropy is conceptually different from the entropy in information theory, it is plausible to assume a close correlation between the two in this context. In a well-ordered, anesthetized state the neurons are obviously likely to have more regular firing patterns that are reflected in a more regular EEG signal than in the more disordered, awake state. If this theory is experimentally proven, it will lend further support to the concept of entropy as a fundamental characteristic of the cerebral state of the brain.
In sum, the following point to the advantages of EEG signal irregularity or complexity characteristics, or entropy, as in indication of the cerebral state of a patient. First, certain forms of entropy have generally been found to behave consistently as a function of anesthetic depth. See the Bruhn et al. and H. E. Viertiö-Oja et al. article “Entropy of EEG signal is a robust index for depth of hypnosis”, Anesthesiology 93 (2000) A, pg. 1369. This warrants consideration of entropy as a natural and robust choice to characterize levels of hypnosis. Second, because entropy correlates with depth of anesthesia at all levels of anesthesia, it avoids the need to combine various subparameters in the manner described in U.S. Pat. Nos. 4,907,597; 5,010,891; 5,320,109; and 5,458,117. Third, the transition from consciousness to unconsciousness takes place at a critical level of entropy which is independent of the patient. Also, and of particular practical significance, recovery of a patient toward consciousness from anesthesia can often be predicted by a rise in entropy toward the critical level. See the Viertio-Oja et al. article in J. Clin. Monitoring and Computing.
A number of techniques and associated algorithms are available for quantifying signal irregularity, including those based on entropy, as described in the Rezek and Roberts article in IEEE Transactions on Biomedical Engineering article. One such algorithm is that which produces spectral entropy for which the entropy values are computed in frequency space. The use of spectral entropy has an advantage of computational simplicity. It also presents the possibility of looking at the contribution of phenomena in various signal frequency ranges, including those of the EEG and EMG (electromylogram), to the entropic characteristics of an indicator for depth of anesthesia.
As hereinafter noted in detail, the computation of spectral entropy as described by Rezek and Roberts is initiated by carrying out a Fourier transform of the EEG signal to obtain a power spectrum. The power spectrum is then normalized over a selected frequency region. In a summation step, the unnormalized spectral entropy corresponding to the frequency range is computed which thereafter is normalized to entropy values in a range between 1 (maximum disorder) and 0 (complete order). The computations are carried out using signal samples or epochs of constant length, for example 5 seconds of data or twelve sequential 5 second epochs (sixty seconds) of data.
The term “spectral entropy” as used herein is deemed to be that computed using the algorithm described by Rezek and Roberts unless otherwise indicated.
While possessing the advantages of computational simplicity, use of the Rezek and Roberts algorithm is attended with certain shortcomings and limitations that affect its accuracy and hence the clinical usefulness of the resulting spectral entropy depth of anesthesia indication. These shortcomings and limitations arise, in part, from the characteristics of the EEG signal data received from the patient to which the algorithm is applied. They also arise, in part, from restraints in the computational criteria under which the Rezek and Roberts calculation can be carried out to determine spectral entropy.
With respect to the EEG signals obtained from the electrodes on the scalp and forehead of the patient, FIG. 1 is a simplistic showing of such signal data. In addition to the burst suppression phenomena shown in FIG. 2, the data will typically contain anomalies or artifacts occurring from non-EEG sources external of the brain. For example, FIG. 3A shows a variation in the EEG signal caused by an eye movement. FIG. 3B shows alterations resulting from eye blinks. It will be readily appreciated that the presence of such artifacts must be taken into consideration if an accurate determination of EEG spectral entropy is to be made. A further source of artifacts occurs if the patient is subjected to electrocautery, as when sealing blood vessels cut in a surgical procedure.
In terms used in signal analysis, EEG signal data containing artifacts are said to be “non-stationary.” A “stationary” signal is one in which statistical properties, such as the mean value, standard deviation, etc. remain constant even though the instantaneous values of the signal vary in an unpredictable way. A “non-stationary” signal is one for which such properties do not remain constant.
The Rezek and Roberts algorithm is one that can only be used, as such, for stationary signals which can be treated with epochs of constant length.
However, if the artifacts occur frequently in the EEG signal data, or the signal shows frequent alteration between bursts and suppression, the amount of pieces of signal that exhibit stationarity and are of a given constant length, for example, the 5 seconds duration described above, is relatively low. Therefore, if data epochs of this length are to be used for computational purposes, a relatively large amount of data must be rejected.
The relative amount of useful data can be increased by decreasing the length of the epochs used for the computations in order to capture only stationary EEG signal data. It will be readily appreciated that it is much easier to obtain data epochs 1 second long between frequent eye movements than 5 second data epochs.
However, epoch length essentially defines the frequency resolution at which the Fourier components for the spectral entropy calculation can be obtained. Specifically, the larger the time duration of the epochs, the better the frequency resolution. Consider a signal that has been sampled with a sampling frequency F, and divided into epochs of length T. The frequency components that can be evaluated under such conditions correspond to the set of frequencies f=1/T, 2/T, 3/T . . . , F/2. The frequency steps 1/T (resolution) are thus determined by the epoch length T. For a signal that has been collected with a 400 Hz sampling frequency, an epoch length of 5 seconds gives frequency components f=0.2 Hz, 0.4 Hz, 0.6 Hz, . . . , 200 Hz, whereas an epoch length of 1 second gives frequency components f=1 Hz, 2 Hz, 3 Hz, . . . 200 Hz. The frequency resolution for 5 second epochs is thus 0.2 Hz whereas the frequency resolution for 1 second epochs is only 1 Hz. A frequency resolution of 0.2 Hz is typically used/desired for EEG signal analysis in order to distinguish among frequencies that correspond to physiologically distinct activity occurring in the brain. This requires 5 second data epochs which, in turn, raise the data collection problem noted above.
A further problem in connection with the use of spectral entropy to determine the depth of anesthesia occurs particularly, in very deep anesthesia, in which the EEG signal is characterized by alternating periods of “bursts” of normal, high frequency and amplitude voltage signals and periods when such signals are suppressed.
When burst suppression occurs in the EEG signal, the spectral entropy computed with the Rezek and Roberts algorithm will remain roughly constant, in contradiction to the deepening anesthesia causing the burst suppression phenomena in the EEG signal. The resulting indication of the entropic state of the brain of a patient is thus higher than it should be and the depth of anesthesia is seen as less, i.e. not as deep, as is actually occurring in the patient. This is a source of potential and serious danger to the patient since it may cause the anesthesiologist/anesthetist to administer additional anesthetic agent to an already heavily anesthetized patient.
FIGS. 4 and 5 illustrate the foregoing phenomena. In FIGS. 4 and 5, the abscissa of the graphs is time. A patient enters a state of deep anesthesia, as by the administration of an anesthetic agent, at about 35 minutes. The patient's EEG evidences burst suppression, as indicated by the rapidly increasing value of the burst suppression ratio (BSR), the BSR being the portion of time the EEG signal is in the suppressed state as a fraction of the sampling period. See FIG. 4 at 50. A typical length for the sampling period is one minute. The ordinate of FIG. 4 is scaled in the burst suppression ratio (BSR) given as a percentage (%) value. A BSR of 100% indicates that the EEG signal is in the suppressed state throughout the sampling period, i.e. for 100% of the sampling period. A BSR of zero indicates that no burst suppression is present. As shown in FIG. 4, as the effects of the anesthetic agent wear off and the depth of anesthesia decreases after the time of 35 minutes, the BSR also decreases as more bursts appear in the EEG signal. Burst suppression ceases at about 45 minutes.
FIG. 5 shows a graph of the entropy values for the patient obtained from the Rezek and Roberts computation of spectral entropy. The ordinate of FIG. 5 is scaled in normalized values of entropy. The graph of entropy 60 in FIG. 5 does not reflect the depth of anesthesia shown by the graph 50 of the BSR in FIG. 4. That is, for a depth of anesthesia following time 35 minutes in the FIGS. 4 and 5 in which the BSR approaches 100%, the hypnotic state of the brain is actually much deeper than that shown in FIG. 5. Or, stated another way, and as shown in FIG. 5, when burst suppression sets in, spectral entropy falls to a generally constant level and remains there as the BSR increases and then decreases as shown in FIG. 4.
The reasons for the phenomenon shown in FIG. 5 are as follows. As noted above, the Fourier transform is carried on a set of sequential EEG signal samples representing a finite block of time, i.e. signals of constant length such as 5 second epochs. An EEG signal of this length will typically contain alternating periods of bursts and suppression. Also, typically, the characteristic frequency fbs corresponding to this alternation between bursts and suppression is less than the lowest frequency f1, of the frequency range [f1, f2] for which the Fourier transform is computed. The lowest frequency f1 used to compute spectral entropy is typically 0.5 Hz and the characteristic frequency fbs of alternation is usually below this frequency. As a result, the power spectrum obtained from the Fourier analysis of the EEG signal samples essentially includes EEG frequency components that are present during the bursts.
While low amplitudes of the power spectrum suggest that suppression is present, this information is lost in the normalization step of the Rezek et al. computation. When the entropy value is summed or integrated in the following step of the Rezek et al. computation, the resulting spectral entropy will have roughly the same value that it would have if the EEG signal had consisted of a continuous burst with no suppression at all. This accounts for the incorrectly high value of the spectral entropy shown as graph 60 in FIG. 5 during the period in which burst suppression is actually present in the EEG signal.
The foregoing problems of EEG signal data collection and spectral entropy computation have raised difficulties in implementing the use of spectral entropy computed by the Rezek and Roberts algorithm as an accurate, useful, and practical indication of the depth of anesthesia.